{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5ce277da-2b4e-45eb-8049-88a75101085a",
   "metadata": {},
   "source": [
    "Chapter 20\n",
    "# 再看邻接矩阵\n",
    "Book_6《数据有道》 | 鸢尾花书：从加减乘除到机器学习"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1205524a-d211-46d0-85f6-6648fc09b78b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8993b852-5026-433f-9e54-942bc63343c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.Graph()\n",
    "# 创建无向图的实例"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a8ac89a9-52e7-447c-a884-e0419c173bfb",
   "metadata": {},
   "outputs": [],
   "source": [
    "G.add_nodes_from(['a', 'b', 'c', 'd', 'e', 'f'])\n",
    "# 添加多个顶点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ff830315-c5cc-4031-acf6-05f0bf2ec429",
   "metadata": {},
   "outputs": [],
   "source": [
    "G.add_edges_from([('a','b'),('a','f'),\n",
    "                  ('a','c'),('a','d'),\n",
    "                  ('d','e'),('c','e'),\n",
    "                  ('d','c'),('b','c'),\n",
    "                  ('b','e'),('b','f'),\n",
    "                  ('e','f'),('c','f')])\n",
    "\n",
    "# 增加一组边"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5444be64-e710-4436-9319-109f7b9005f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 城市具体位置\n",
    "\n",
    "pos = {'a':(50.6463,6.5692),\n",
    "       'b':(70.3019,41.0777),\n",
    "       'c':(35.6363,36.0673),\n",
    "       'd':(6.8205,16.8171),\n",
    "       'e':(26.1044,68.8277),\n",
    "       'f':(59.1871,69.6398)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9dbc9e10-903e-4e38-acfc-daa46db10387",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (6,6))\n",
    "nx.draw_networkx(G, \n",
    "                 pos = pos,\n",
    "                 node_size = 180)\n",
    "plt.savefig('城市位置.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4dbbfc9e-5e6d-4f00-8d96-c7566754239c",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = nx.adjacency_matrix(G).todense()\n",
    "# 无向图的邻接矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b80d4fa4-0909-46d6-adb9-399888a8b664",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 1, 1, 0, 1],\n",
       "       [1, 0, 1, 0, 1, 1],\n",
       "       [1, 1, 0, 1, 1, 1],\n",
       "       [1, 0, 1, 0, 1, 0],\n",
       "       [0, 1, 1, 1, 0, 1],\n",
       "       [1, 1, 1, 0, 1, 0]], dtype=int32)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7a8698f0-1c39-4772-bf12-5640d43802c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A,square = True, \n",
    "            cmap = 'Blues',\n",
    "            annot = True, fmt = '.0f',\n",
    "            xticklabels = list(G.nodes), \n",
    "            yticklabels = list(G.nodes),\n",
    "            linecolor = 'k', linewidths = 0.2)\n",
    "plt.savefig('无向图的邻接矩阵A.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2cf71b94-e4f5-4e8a-97c0-5c0cbbcbaf01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[4., 2., 3., 1., 4., 2.],\n",
       "        [2., 4., 3., 3., 2., 3.],\n",
       "        [3., 3., 5., 2., 3., 3.],\n",
       "        [1., 3., 2., 3., 1., 3.],\n",
       "        [4., 2., 3., 1., 4., 2.],\n",
       "        [2., 3., 3., 3., 2., 4.]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A @ A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7bd13bb1-3c1f-4d3c-9d61-7eeaa856ef65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAegAAAGiCAYAAAAsk1UGAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8g+/7EAAAACXBIWXMAAA9hAAAPYQGoP6dpAAA6b0lEQVR4nO3de1xU1d4/8M8GZECEEUS5iCIqoYiU0kVIjpaalZrak+c8diF90NNFC0RN6WgX7TQmGtnJexllx+OjddJfZppHA1PQvEBHwPsNNUBSREEYgZnfHz7SmeQ2ODNr9qzPu9d+vZrF7L2/yz2LL9+19+ytGI1GI4iIiMiuOIkOgIiIiG7HBE1ERGSHmKCJiIjsEBM0ERGRHWKCJiIiskNM0ERERHaICZqIiMgOMUETERHZISZoIiIiO8QETUREZIeYoImIiBrw1ltvQVEUk6VHjx6NrrN+/Xr06NEDbm5u6N27NzZv3tyifTNBExERNaJXr14oLCysW3bt2tXgezMzMzF27FjEx8cjOzsbo0aNwqhRo5Cbm2v2fhU+LIOIiKh+b731FjZs2ICcnJxmvf9Pf/oTKioqsGnTprq2fv364Z577sGyZcvM2jcraCIiko5er8fVq1dNFr1eX+97jx8/jsDAQHTt2hXPPPMMCgoKGtxuVlYWBg8ebNI2dOhQZGVlmR2ji9lrWImiKKJDICKiFrLFZKx7n8kW29aMkb54++23TdrefPNNvPXWWyZtDzzwANLS0hAWFobCwkK8/fbbiI2NRW5uLjw9PW/bblFREfz8/Eza/Pz8UFRUZHaMdpOgAaBL4qam3+QgznwwHACQebxUcCS2FRPqDQB4+Z/5giOxrSVPhgMAKqvlOaPk3urmH90yjWtAzrF9a1xbnWK5Sd/k5GQkJSWZtGk0mtve99hjj9X9f2RkJB544AEEBwdj3bp1iI+Pt1g89bGrBE1ERGQLGo2m3oTclLZt2+Kuu+7CiRMn6v25v78/iouLTdqKi4vh7+9v9r54DpqIiNRBUSy3tFB5eTlOnjyJgICAen8eHR2N7du3m7Rt27YN0dHRZu+LCZqIiNRBcbLc0kzTpk1DRkYGzpw5g8zMTIwePRrOzs4YO3YsACAuLg7Jycl1709ISMCWLVuwcOFCHDlyBG+99Rb279+PyZPNP3/OKW4iIlIHARcTnz9/HmPHjsWlS5fQvn179O/fH3v27EH79u0BAAUFBXBy+i3hx8TEYM2aNZg1axZef/11hIaGYsOGDYiIiDB730zQREREDVi7dm2jP09PT7+tbcyYMRgzZswd75sJmoiI1MGCV3GrARM0ERGpg2T3y5DrzxEiIiKVYAVNRETqwCluIiIiO8QpbiIiIhKNFTQREakDp7iJiIjsEKe4iYiISDRW0EREpA6c4iYiIrJDkk1xM0ETEZE6SFZBy9VbIiIilWAFTURE6iBZBc0ETURE6uAk1zlouf4cISIiUglW0EREpA6c4iYiIrJD/JqVfF4c1A0zhvfAqozTmLshX3Q4VrNpXRoOZKaj8PxZtHLVoHvP3vjj+MkICAoWHZrVxIa0RWyIN3xatwIAFF7T47sjvyK/uEJwZNZ1YP8+pK36BIfzc1FSUoLUDxfj4UGDRYdlUxzXjjuuZSHXfEE9Ijtp8XR0Zxy+cFV0KFZ35FA2Hh72FGYv/ATT3/kQtTU1WDDrVeirKkWHZjWllTXYmHcR7/1wGvPTz+BYyXW80K8TAjxdRYdmVZWV1xEWFobkWW+KDkUIjmsHHdeKk+UWFZC6gm7t6owPnr0Hyev+jclDQkWHY3XT5i4yeT0h6Q28+vSjOHPiCMIi+giKyrpyi8pNXn+TX4LYEG908XFH4bUbgqKyvv6xA9A/doDoMITguHbgcS3ZFLc6/oywkjlPRWDH4YvYfeyS6FCEqKy4mbw82ngJjsQ2FABRHb3g6qzg9GUHrC4IAMe1bOPakd1RBZ2fn4+CggLcuGFaiTzxxBONrqfX66HX6+9k13dseJ8A9OrohZGpu4XGIYrBYMCaFakIDY9EUJduosOxqkAvDaYN6AIXJwX6GgNW7j2PIgeunmXGce3g41olU9OW0qIEferUKYwePRqHDh2CoigwGo0AAOX/ph9qa2sbXV+n0+Htt99uya4tIqCtG94c3QvPLd2LGzUGYXGItHppCs6fPYW/pCwXHYrVFV/TQ7fjFNxaOaNPoCeeiwrEBz+eZZJ2MBzXEoxryaa4W5SgExISEBISgu3btyMkJAQ//fQTLl26hKlTp2LBggVNrp+cnIykpCSTNq1W25JQWiQiSAtfTw2+mdq/rs3F2Qn3d/VBXP9ghE3/DgajzcKxudVLU/DzT7uQ/N5y+Pj6iQ7H6mqNQElFNYBqnLtShWBvdzzUzQf/yCkSHRpZEMe1BOOaFXTTsrKysGPHDvj6+sLJyQlOTk7o378/dDodXn31VWRnZze6vkajgUajaVHAlpB5/FcMfS/DpG3+2Ltx6mI5lm0/6bCD2Gg04otlC3AgKwMzdUvQ3j9QdEhCKArgItktA2XAcS33uHZELUrQtbW18PT0BAD4+vril19+QVhYGIKDg3H06FGLBmgNFfpaHPvd1b2VN2pRWlF9W7sjWb0kBVkZW5EwOwVu7h64cvnmRTStPTzgqnETHJ11PBHeHvnF5bhcWQM3FyfcG+SFUN/WWLz7nOjQrOp6RQUKCgrqXl84fx5HDh+GVqtFQKBj/gLnuJZgXHOKu2kRERH4+eefERISggceeADz58+Hq6srVqxYga5du1o6RrKQHZu/AgDMm/mSSXt84mzEDhkuIiSr89S4IC4qEF5uLqiqMeBCmR6Ld5/DkRLHvlFJXl4uJoyPq3u9YL4OAPDEyNGY++48UWGRFUg1rjnF3bRZs2ahouLmL7g5c+Zg+PDhiI2NRbt27fC///u/Fg3QVsYu3iM6BKtL+3av6BBs7u/ZhaJDEOK++x/Az3n2P5tlbRzXpGYtStBDhw6t+//u3bvjyJEjuHz5Mry9veuu5CYiIrIoyfKLxe4k5uPjY6lNERER3U6yKW65ektERKQSUt+Lm4iIVESyCpoJmoiI1EGyc9By/TlCRESkEkzQRESkDnbwPOh58+ZBURQkJiY2+J60tDQoimKyuLmZf9MYTnETEZE6CJ7i3rdvH5YvX47IyMgm3+vl5WVyZ82WfAWZFTQREamDwAq6vLwczzzzDFauXAlvb++mQ1UU+Pv71y1+fuY/wIQJmoiIpKPX63H16lWTRa/XN/j+SZMmYdiwYRg8eHCztl9eXo7g4GB06tQJI0eORF5entkxMkETEZE6KIrFFp1OB61Wa7LodLp6d7t27VocPHiwwZ//XlhYGFatWoWNGzfiiy++gMFgQExMDM6fP29Wd3kOmoiIVMGSt5JOTk5GUlKSSVt9j0E+d+4cEhISsG3btmZf6BUdHY3o6Oi61zExMejZsyeWL1+OuXPnNjtGJmgiIpKORqOpNyH/3oEDB3Dx4kX07du3rq22thY7d+7ERx99BL1eD2dn50a30apVK/Tp0wcnTpwwK0YmaCIiUgURD2MaNGgQDh06ZNI2fvx49OjRAzNmzGgyOQM3E/qhQ4fw+OOPm7VvJmgiIlIHAd+y8vT0REREhEmbh4cH2rVrV9ceFxeHjh071p2jnjNnDvr164fu3bvjypUrSElJwdmzZzFhwgSz9s0ETUREdAcKCgrg5PTbNdelpaWYOHEiioqK4O3tjaioKGRmZiI8PNys7TJBExGRKoiY4q5Penp6o69TU1ORmpp6x/thgiYiIlWwlwRtK/weNBERkR1iBU1ERKogWwXNBE1ERKrABE1ERGSP5MrPPAdNRERkj1hBExGRKsg2xa0YjUaj6CAA+f7hiYgciS1Sifezf7fYtkq/eMZi27IWTnETERHZIbua4s48Xio6BJuJCfUGAHRJ3CQ4Ets688FwAMDL/8wXHIltLXny5i3+ZOr3rT7LNK6B38a2jMfa2mSbabWrBE1ERNQQ2RI0p7iJiIjsECtoIiJSB7kKaCZoIiJSB05xExERkXCsoImISBVkq6CZoImISBWYoImIiOyRXPmZ56CJiIjsEStoIiJSBU5xExER2SHZEjSnuImIiOwQK2giIlIF2SpoJmgiIlIF2RI0p7iJiIjsECtoIiJSB7kKaCZoIiJSB05xExERkXCsoImISBVkq6CZoImISBWYoImIiOyRXPmZ56CJiIjsEStoIiJSBU5xExER2SEmaAlsWpeGA5npKDx/Fq1cNejeszf+OH4yAoKCRYdmMy8O6oYZw3tgVcZpzN2QLzocq4kNaYvYEG/4tG4FACi8psd3R35FfnGF4MisS9Z+yzi2ZT3WMpDyHPSRQ9l4eNhTmL3wE0x/50PU1tRgwaxXoa+qFB2aTUR20uLp6M44fOGq6FCsrrSyBhvzLuK9H05jfvoZHCu5jhf6dUKAp6vo0KxK1n7LOLZlOtaKolhsaal58+ZBURQkJiY2+r7169ejR48ecHNzQ+/evbF582az9yVlgp42dxFihwxHx+Cu6Nz1LkxIegOXSopw5sQR0aFZXWtXZ3zw7D1IXvdvlFVWiw7H6nKLypFXXIGSimpcLL+Bb/JLoK8xoIuPu+jQrErWfss4tmU61qIT9L59+7B8+XJERkY2+r7MzEyMHTsW8fHxyM7OxqhRozBq1Cjk5uaatb87TtBGoxFGo/FONyNUZUU5AMCjjZfgSKxvzlMR2HH4InYfuyQ6FJtTAER19IKrs4LTlx23ovo9WfsNyDW2AbmPtbWVl5fjmWeewcqVK+Ht7d3oexctWoRHH30U06dPR8+ePTF37lz07dsXH330kVn7bPE56E8++QSpqak4fvw4ACA0NBSJiYmYMGFCk+vq9Xro9fqW7tqiDAYD1qxIRWh4JIK6dBMdjlUN7xOAXh29MDJ1t+hQbCrQS4NpA7rAxUmBvsaAlXvPo+jaDdFhWZ2s/b5FprEtzbG24DVi9eUhjUYDjUZT7/snTZqEYcOGYfDgwXjnnXca3XZWVhaSkpJM2oYOHYoNGzaYFWOLKug33ngDCQkJGDFiBNavX4/169djxIgRmDJlCt54440m19fpdNBqtSaLKKuXpuD82VN4aUbj/+BqF9DWDW+O7oUpX+TgRo1BdDg2VXxND92OU0jJOIMfT5fiuahA+Dvg+bnfk7Xft8gytgF5jrUlp7jry0M6na7e/a5duxYHDx5s8Oe/V1RUBD8/P5M2Pz8/FBUVmdXfFlXQS5cuxcqVKzF27Ni6tieeeAKRkZF45ZVXMGfOnEbXT05Ovu2vCxFJevXSFPz80y4kv7ccPr5+Ta+gYhFBWvh6avDN1P51bS7OTri/qw/i+gcjbPp3MKj7TEWDao1ASUU1gGqcu1KFYG93PNTNB//IMW+wqI2s/QbkGtuA3Me6perLQ/VVz+fOnUNCQgK2bdsGNzc3W4UHoIUJurq6Gvfee+9t7VFRUaipqWly/camEWzBaDTii2ULcCArAzN1S9DeP1BYLLaSefxXDH0vw6Rt/ti7cepiOZZtP+mwybk+igK4OMn1fUpAjn7LOLbr46jH2pLfg25uHjpw4AAuXryIvn371rXV1tZi586d+Oijj6DX6+Hs7Gyyjr+/P4qLi03aiouL4e/vb1aMLZrifu6557B06dLb2lesWIFnnnmmJZu0qdVLUpD5wxa8OH0O3Nw9cOXyJVy5fAk39FWiQ7OaCn0tjhWVmyyVN2pRWlGNY0XlosOzmifC26N7O3f4tG6FQC8Nnghvj1Df1th3zrG/YiZrv2Uc2zIda0Wx3NJcgwYNwqFDh5CTk1O33HvvvXjmmWeQk5NzW3IGgOjoaGzfvt2kbdu2bYiOjjarv82uoP9zKkBRFHz88cf4/vvv0a9fPwDA3r17UVBQgLi4OLMCEGHH5q8AAPNmvmTSHp84G7FDhosIiazEU+OCuKhAeLm5oKrGgAtleizefQ5HShz7Jg6y9lvGsS3TsRZxJzFPT09ERESYtHl4eKBdu3Z17XFxcejYsWPdOeqEhAQMGDAACxcuxLBhw7B27Vrs378fK1asMGvfzU7Q2dnZJq+joqIAACdPngQA+Pr6wtfXF3l5eWYFIELat3tFh2AXxi7eIzoEq/t7dqHoEISQtd8yjm1Zj7U9KSgogJPTbxPSMTExWLNmDWbNmoXXX38doaGh2LBhw22JvinNTtA//PCDWRsmIiKyJHu5FXd6enqjrwFgzJgxGDNmzB3tR8p7cRMRkfrI9rAMKW/1SUREZO9YQRMRkSpIVkAzQRMRkTo4OeB3uxvDKW4iIiI7xAqaiIhUgVPcREREdohXcRMREZFwrKCJiEgVJCugmaCJiEgdZJviZoImIiJVkC1B8xw0ERGRHWIFTUREqiBZAc0ETURE6sApbiIiIhKOFTQREamCZAU0EzQREakDp7iJiIhIOFbQRESkCpIV0EzQRESkDpziJiIiIuFYQRMRkSpIVkAzQRMRkTrINsWtGI1Go+ggAPn+4YmIHIktUkm/eRkW29aemQMsti1r4TloIiIiO2RXU9wv/zNfdAg2s+TJcABy9Rn4rd9u90wSHIltVeUsBgBkHi8VHIntxIR6A5D3My5Tv2/12dpkm2m1qwRNRETUEMnyM6e4iYiI7BEraCIiUgVOcRMREdkhyfIzp7iJiIjsEStoIiJSBU5xExER2SHZEjSnuImIiOwQK2giIlIFyQpoJmgiIlIHTnETERHZIUWx3NJcS5cuRWRkJLy8vODl5YXo6Gh89913Db4/LS0NiqKYLG5ubi3qLytoIiKiBgQFBWHevHkIDQ2F0WjEZ599hpEjRyI7Oxu9evWqdx0vLy8cPXq07nVLK38maCIiUgVLTnHr9Xro9XqTNo1GA41GY9I2YsQIk9d//etfsXTpUuzZs6fBBK0oCvz9/e84Rk5xExGRKlhyilun00Gr1ZosOp2u0f3X1tZi7dq1qKioQHR0dIPvKy8vR3BwMDp16oSRI0ciLy+vRf1lBU1ERNJJTk5GUlKSSdvvq+dbDh06hOjoaFRVVaFNmzb4+uuvER5e/yM2w8LCsGrVKkRGRqKsrAwLFixATEwM8vLyEBQUZFaMTNBERKQKThac4q5vOrshYWFhyMnJQVlZGb788ks8//zzyMjIqDdJR0dHm1TXMTEx6NmzJ5YvX465c+eaFSMTNBERqYKob1m5urqie/fuAICoqCjs27cPixYtwvLly5tct1WrVujTpw9OnDhh9n55DpqIiMgMBoPhtgvMGlJbW4tDhw4hICDA7P2wgiYiIlUQcaOS5ORkPPbYY+jcuTOuXbuGNWvWID09HVu3bgUAxMXFoWPHjnUXmM2ZMwf9+vVD9+7dceXKFaSkpODs2bOYMGGC2ftmgiYiIlVwEjDFffHiRcTFxaGwsBBarRaRkZHYunUrhgwZAgAoKCiAk9Nvk9GlpaWYOHEiioqK4O3tjaioKGRmZjZ4UVljmKCJiEgVRFTQn3zySaM/T09PN3mdmpqK1NRUi+yb56CJiIjsECtoIiJSBcmelSFngo4NaYvYEG/4tG4FACi8psd3R35FfnGF4MisS8Z+/+WFxzHrxcdN2o6eLsI9T74jKCLb2LQuDQcy01F4/ixauWrQvWdv/HH8ZAQEBYsOzapk/IzL1GcFcmVoKRN0aWUNNuZdxMXyG1AUBQ901uKFfp0wb8cpFF67ITo8q5G133knfsGwF/9W97qm1iAwGts4cigbDw97Cl3vCkdtbQ2+/GwpFsx6Fe8uWwuNm7vo8KxGxs+4jH2WhZQJOreo3OT1N/kliA3xRhcfd4f+QMva75paA4ovXRMdhk1Nm7vI5PWEpDfw6tOP4syJIwiL6CMoKuuT8TMuU59FXMUtkpQJ+j8pAPp29IKrs4LTlytFh2MzMvW7e+f2OPX9X1Glr8bef5/GG3/7fzhXVCo6LJuqrLj5S9yjjZfgSGxHps/4LY7eZxFXcYvUogSt0+ng5+eH//mf/zFpX7VqFUpKSjBjxgyLBGdNgV4aTBvQBS5OCvQ1Bqzcex5FDvbXZn1k6/e+3DP48xtf4NjZYvj7avGXFx7Dv1ZNQdRTf0X59ebdCUjtDAYD1qxIRWh4JIK6dBMdjtXJ9hkH5OyzDFr0Navly5ejR48et7X36tULy5Yta3J9vV6Pq1evmiy2VnxND92OU0jJOIMfT5fiuahA+Hu62jwOW5Ot39/vzsc//5WN3OO/4F9ZhzFq8lJo27jjvx7pKzo0m1m9NAXnz57CSzMc+8K4W2T7jAPy9NmSj5tUgxYl6KKionrvK9q+fXsUFhY2uX59z+G0tVojUFJRjXNXqvD/8ktwoUyPh7r52DwOW5O137eUlVfiRMFFdOvUXnQoNrF6aQp+/mkXZuqWwMfXT3Q4NiHjZ1yWPjspisUWNWhRgu7UqRN27959W/vu3bsRGBjY5PrJyckoKyszWURTFMBFtisQIF+/PdxdERLki6JfxX/mrMloNGL10hQcyMrAa+8uRnv/pselo5LtMw7I2WdH1KJz0BMnTkRiYiKqq6vx8MMPAwC2b9+O1157DVOnTm1yfXOew2kNT4S3R35xOS5X1sDNxQn3Bnkh1Lc1Fu8+JywmW5Cx37opo/HtzkMo+OUyAjtoMevFYag1GLBuywHRoVnV6iUpyMrYioTZKXBz98CVy5cAAK09POCqcRMcnfXI+BmXqc8qKXwtpkUJevr06bh06RJefvll3Lhx80IENzc3zJgxA8nJyRYN0Bo8NS6IiwqEl5sLqmoMuFCmx+Ld53CkxPG+2P+fZOx3R7+2+Fw3Hj7a1vi1tByZOacwIG4hfi0tb3plFdux+SsAwLyZL5m0xyfORuyQ4SJCsgkZP+My9ZlXcTeDoih47733MHv2bBw+fBju7u4IDQ0VWhWb4+/ZTZ8nd0Qy9jtu5qeiQxAi7du9okMQQsbPuEx9liw/39n3oNu0aYP77rvPUrEQERHR/5H+RiVERKQOarn62lKYoImISBXkSs98HjQREZFdYgVNRESqwKu4iYiI7JBs917hFDcREZEdYgVNRESqwCluIiIiOyRZfuYUNxERkT1iBU1ERKrAKW4iIiI7JNtV3EzQRESkCrJV0DwHTUREZIdYQRMRkSrIVT8zQRMRkUrI9jQrTnETERHZIVbQRESkCpIV0EzQRESkDryKm4iIiIRjBU1ERKogWQHNBE1EROrAq7iJiIgIALB06VJERkbCy8sLXl5eiI6OxnfffdfoOuvXr0ePHj3g5uaG3r17Y/PmzS3aNxM0ERGpgqJYbmmuoKAgzJs3DwcOHMD+/fvx8MMPY+TIkcjLy6v3/ZmZmRg7dizi4+ORnZ2NUaNGYdSoUcjNzTW/v0aj0Wj2WlYg29V5RESOxBapZNLXhy22rfcf7wq9Xm/SptFooNFomlzXx8cHKSkpiI+Pv+1nf/rTn1BRUYFNmzbVtfXr1w/33HMPli1bZlaMrKCJiEgVnCy46HQ6aLVak0Wn0zW6/9raWqxduxYVFRWIjo6u9z1ZWVkYPHiwSdvQoUORlZVldn/t6iKxymq7KOZtwr3VzRmDl/+ZLzgS21ryZDgAIPN4qeBIbCsm1BuAXMf71rGWaVwDco7tW8daTZKTk5GUlGTS1lD1fOjQIURHR6Oqqgpt2rTB119/jfDw+vtcVFQEPz8/kzY/Pz8UFRWZHaNdJWgiIqKGWPJUaHOnswEgLCwMOTk5KCsrw5dffonnn38eGRkZDSZpS2GCJiIiVXASdKmSq6srunfvDgCIiorCvn37sGjRIixfvvy29/r7+6O4uNikrbi4GP7+/mbvl+egiYiIzGAwGG67wOyW6OhobN++3aRt27ZtDZ6zbgwraCIiUgURFXRycjIee+wxdO7cGdeuXcOaNWuQnp6OrVu3AgDi4uLQsWPHugvMEhISMGDAACxcuBDDhg3D2rVrsX//fqxYscLsfTNBExGRKoj4Ou7FixcRFxeHwsJCaLVaREZGYuvWrRgyZAgAoKCgAE5Ov01Gx8TEYM2aNZg1axZef/11hIaGYsOGDYiIiDB730zQREREDfjkk08a/Xl6evptbWPGjMGYMWPueN9M0EREpAqiLhIThQmaiIhUQbYbTvIqbiIiIjvECpqIiFRBtsdNMkETEZEqyDblywRNRESqIFkBLd0fJERERKrACpqIiFSB56CJiIjskGT5mVPcRERE9ogVNBERqQLvJEZERGSHZDsHzSluIiIiO8QKmoiIVEGyApoJmoiI1EG2c9Cc4iYiIrJDrKCJiEgVFMhVQjNBExGRKsg2xS1tgj6wfx/SVn2Cw/m5KCkpQeqHi/HwoMGiw7Kq2JC2iA3xhk/rVgCAwmt6fHfkV+QXVwiOzHo2rUvDgcx0FJ4/i1auGnTv2Rt/HD8ZAUHBokOzKhmPNcBxDTj2sZYtQUt7Drqy8jrCwsKQPOtN0aHYTGllDTbmXcR7P5zG/PQzOFZyHS/064QAT1fRoVnNkUPZeHjYU5i98BNMf+dD1NbUYMGsV6GvqhQdmlXJeKwBjmuZjrUMpK2g+8cOQP/YAaLDsKnconKT19/klyA2xBtdfNxReO2GoKisa9rcRSavJyS9gVeffhRnThxBWEQfQVFZn4zHGuC4Bhz7WCuSfc9K2gQtOwVA345ecHVWcPqyY1eT/6my4uYvM482XoIjsR1Zj7WMHP1YyzbF3ewEnZSU1OyNvv/++43+XK/XQ6/XN3t7ZDmBXhpMG9AFLk4K9DUGrNx7HkUO9ld2QwwGA9asSEVoeCSCunQTHY7VyXysZcNj7ZianaCzs7NNXh88eBA1NTUICwsDABw7dgzOzs6Iiopqcls6nQ5vv/22maGSJRRf00O34xTcWjmjT6AnnosKxAc/npViMK9emoLzZ0/hLynLRYdiEzIfa9nIcqwlm+FufoL+4Ycf6v7//fffh6enJz777DN4e3sDAEpLSzF+/HjExsY2ua3k5OTbKnKtVtvcUOgO1BqBkopqANU4d6UKwd7ueKibD/6RUyQ6NKtavTQFP/+0C8nvLYePr5/ocGxC1mMtI1mOtWwPy2jROeiFCxfi+++/r0vOAODt7Y133nkHjzzyCKZOndro+hqNBhqNpiW7JgtTFMDFgU/sGI1GfLFsAQ5kZWCmbgna+weKDkkYRz/W9Bsea8fQogR99epVlJSU3NZeUlKCa9eu3XFQtnC9ogIFBQV1ry+cP48jhw9Dq9UiINAxf4k/Ed4e+cXluFxZAzcXJ9wb5IVQ39ZYvPuc6NCsZvWSFGRlbEXC7BS4uXvgyuVLAIDWHh5w1bgJjs56ZDzWAMe1ox9r2f7maFGCHj16NMaPH4+FCxfi/vvvBwDs3bsX06dPx5NPPmnRAK0lLy8XE8bH1b1eMF8HAHhi5GjMfXeeqLCsylPjgrioQHi5uaCqxoALZXos3n0OR0oc74YGt+zY/BUAYN7Ml0za4xNnI3bIcBEh2YSMxxrguHb0Yy3ZDHfLEvSyZcswbdo0PP3006iurr65IRcXxMfHIyUlxaIBWst99z+An/OOig7Dpv6eXSg6BJtL+3av6BCEkPFYAxzX5FhalKBbt26NJUuWICUlBSdPngQAdOvWDR4eHhYNjoiI6BYnPiyj+Tw8PBAZGWmpWIiIiBrEKW4iIiI7JNtFYtI+LIOIiMiesYImIiJV4I1KiIiI7JBk+ZlT3ERERA3R6XS477774OnpiQ4dOmDUqFE4erTxr/KlpaVBURSTxc3N/BsjMUETEZEqOCmKxZbmysjIwKRJk7Bnzx5s27YN1dXVeOSRR1BR0fiNYLy8vFBYWFi3nD171uz+coqbiIhUQcQU95YtW0xep6WloUOHDjhw4AD+8Ic/NLieoijw9/e/o32zgiYiIuno9XpcvXrVZNHr9U2uV1ZWBgDw8fFp9H3l5eUIDg5Gp06dMHLkSOTl5ZkdIxM0ERGpgpMFF51OB61Wa7LodLpG928wGJCYmIgHH3wQERERDb4vLCwMq1atwsaNG/HFF1/AYDAgJiYG58+fN6u/nOImIiJVUCw4x52cnIykpCSTtqYegzxp0iTk5uZi165djb4vOjoa0dHRda9jYmLQs2dPLF++HHPnzm12jEzQREQkHY1G02RC/k+TJ0/Gpk2bsHPnTgQFBZm1r1atWqFPnz44ceKEWetxipuIiFRBseDSXEajEZMnT8bXX3+NHTt2ICQkxOy4a2trcejQIQQEBJi1HitoIiJSBRF3Eps0aRLWrFmDjRs3wtPTE0VFRQAArVYLd3d3AEBcXBw6duxYdw57zpw56NevH7p3744rV64gJSUFZ8+exYQJE8zaNxM0ERGpgogbiS1duhQAMHDgQJP2Tz/9FOPGjQMAFBQUwMnptwnp0tJSTJw4EUVFRfD29kZUVBQyMzMRHh5u1r6ZoImIiBpgNBqbfE96errJ69TUVKSmpt7xvpmgiYhIFWS7FzcTNBERqYIlv2alBryKm4iIyA6xgiYiIlWQraJkgiYiIlXgFDcREREJxwqaiIhUQa76GVCMzfmSlw3INnVBRORIbJFKvvy50GLbeupu8267KQKnuImIiOyQXU1xd0ncJDoEmznzwXAAQObxUsGR2FZMqDcA4OV/5guOxLaWPHnzFn+V1XYxYWUT7q1uzorJNK4BOcf2rXFtbbJVlHaVoImIiBoi26lQJmgiIlIFudKzfDMGREREqsAKmoiIVEGyGW4maCIiUgcnySa5OcVNRERkh1hBExGRKnCKm4iIyA4pnOImIiIi0VhBExGRKnCKm4iIyA7xKm4iIiISjhU0ERGpAqe4iYiI7BATNBERkR3i16yIiIhIOFbQRESkCk5yFdBM0EREpA6c4iYiIiLhWEETEZEq8CpuIiIiO8QpbiIiIhKOFTQREakCr+ImIiKyQ7JNcTNBA3hxUDfMGN4DqzJOY+6GfNHhWM2mdWk4kJmOwvNn0cpVg+49e+OP4ycjIChYdGhWExvSFrEh3vBp3QoAUHhNj++O/Ir84grBkVnXgf37kLbqExzOz0VJSQlSP1yMhwcNFh2WTXFcO+64loX056AjO2nxdHRnHL5wVXQoVnfkUDYeHvYUZi/8BNPf+RC1NTVYMOtV6KsqRYdmNaWVNdiYdxHv/XAa89PP4FjJdbzQrxMCPF1Fh2ZVlZXXERYWhuRZb4oORQiOa8cc14piuaW5dDod7rvvPnh6eqJDhw4YNWoUjh492uR669evR48ePeDm5obevXtj8+bNZvdX6gTd2tUZHzx7D5LX/RtlldWiw7G6aXMXIXbIcHQM7orOXe/ChKQ3cKmkCGdOHBEdmtXkFpUjr7gCJRXVuFh+A9/kl0BfY0AXH3fRoVlV/9gBmJwwBYMGDxEdis1xXDvuuFYsuDRXRkYGJk2ahD179mDbtm2orq7GI488goqKhmfhMjMzMXbsWMTHxyM7OxujRo3CqFGjkJuba1Z/W5ygf/zxRzz77LOIjo7GhQsXAACrV6/Grl27WrpJm5vzVAR2HL6I3ccuiQ5FiMqKcgCARxsvwZHYhgIgqqMXXJ0VnL7seNUF3cRx7bjj2klRLLY015YtWzBu3Dj06tULd999N9LS0lBQUIADBw40uM6iRYvw6KOPYvr06ejZsyfmzp2Lvn374qOPPjKvv2a9+/989dVXGDp0KNzd3ZGdnQ29Xg8AKCsrw7vvvtvk+nq9HlevXjVZbG14nwD06uiF+ZuanqpwRAaDAWtWpCI0PBJBXbqJDseqAr00eH9EGBaN7IH/vscfK/eeR9G1G6LDIivguJZnXN+p+vLQrVzWmLKyMgCAj49Pg+/JysrC4MGm13wMHToUWVlZZsXYogT9zjvvYNmyZVi5ciVatWpV1/7ggw/i4MGDTa6v0+mg1WpNFlsKaOuGN0f3wpQvcnCjxmDTfduL1UtTcP7sKbw04x3RoVhd8TU9dDtOISXjDH48XYrnogLh7+DnoGXEce3449qSU9z15SGdTtfo/g0GAxITE/Hggw8iIiKiwfcVFRXBz8/PpM3Pzw9FRUVm9bdFV3EfPXoUf/jDH25r12q1uHLlSpPrJycnIykp6bZ1bSUiSAtfTw2+mdq/rs3F2Qn3d/VBXP9ghE3/DgajzcKxudVLU/DzT7uQ/N5y+Pj6Nb2CytUagZKKagDVOHelCsHe7niomw/+kWPeYCH7xnEtwbi24Les6stDGo2m0XUmTZqE3Nxcm53KbVGC9vf3x4kTJ9ClSxeT9l27dqFr165Nrq/RaJr8h7CmzOO/Yuh7GSZt88fejVMXy7Fs+0mHHcRGoxFfLFuAA1kZmKlbgvb+gaJDEkJRABfZ7nggAY5ruce1uczNQ5MnT8amTZuwc+dOBAUFNfpef39/FBcXm7QVFxfD39/frBhblKAnTpyIhIQErFq1Coqi4JdffkFWVhamTZuG2bNnt2STNlWhr8WxonKTtsobtSitqL6t3ZGsXpKCrIytSJidAjd3D1y5fPMimtYeHnDVuAmOzjqeCG+P/OJyXK6sgZuLE+4N8kKob2ss3n1OdGhWdb2iAgUFBXWvL5w/jyOHD0Or1SIg0DF/gXNcO/64FnGjEqPRiFdeeQVff/010tPTERIS0uQ60dHR2L59OxITE+vatm3bhujoaLP23aIEPXPmTBgMBgwaNAjXr1/HH/7wB2g0GkybNg2vvPJKSzZJNrBj81cAgHkzXzJpj0+cjdghw0WEZHWeGhfERQXCy80FVTUGXCjTY/HuczhS4tg3KsnLy8WE8XF1rxfMv3lu7YmRozH33XmiwiIrkGlci3ia1aRJk7BmzRps3LgRnp6edeeRtVot3N1vfl0zLi4OHTt2rDuHnZCQgAEDBmDhwoUYNmwY1q5di/3792PFihVm7VsxGo0tnvi5ceMGTpw4gfLycoSHh6NNmzYt3RQURUGXxE0tXl9tznxwc+BkHi8VHIltxYR6AwBe/qfj3tmpPkueDAcAVFY76DxrPdxb3fxtKtO4BuQc2zGh3riDVNJsP50qs9i27u/avOuelAb+Kvj0008xbtw4AMDAgQPRpUsXpKWl1f18/fr1mDVrFs6cOYPQ0FDMnz8fjz/+uFkx3tGtPl1dXREeHn4nmyAiImoWEVeONOcPj/T09NvaxowZgzFjxtzRvnkvbiIiUgfJru2U+lafRERE9ooVNBERqQIfN0lERGSHRFzFLRITNBERqYJk+ZnnoImIiOwRK2giIlIHyUpoJmgiIlIF2S4S4xQ3ERGRHWIFTUREqsCruImIiOyQZPmZU9xERET2iBU0ERGpg2QlNBM0ERGpAq/iJiIiIuFYQRMRkSrwKm4iIiI7JFl+ZoImIiKVkCxD8xw0ERGRHWIFTUREqiDbVdxM0EREpAqyXSTGKW4iIiI7xAqaiIhUQbICGorRaDSKDgIAFNnmLoiIHIgtUsnhwgqLbatngIfFtmUtnOImIiKyQ3Y1xZ15vFR0CDYTE+oNAHj5n/mCI7GtJU+GA2C/ZXCrzzKNa+C3sd0lcZPgSGznzAfDbbIfXsVNRERkh2Q7E8opbiIiIjvECpqIiFRBsgKaCZqIiFRCsgzNBE1ERKog20ViPAdNRERkh1hBExGRKsh2FTcTNBERqYJk+ZlT3ERERPaICZqIiNRBseBihp07d2LEiBEIDAyEoijYsGFDo+9PT0+Hoii3LUVFRWbtlwmaiIhUQbHgf+aoqKjA3XffjcWLF5u13tGjR1FYWFi3dOjQwaz1eQ6aiIioEY899hgee+wxs9fr0KED2rZt2+L9soImIiJVUBTLLXq9HlevXjVZ9Hq9ReO95557EBAQgCFDhmD37t1mr88ETUREqmDJU9A6nQ5ardZk0el0FokzICAAy5Ytw1dffYWvvvoKnTp1wsCBA3Hw4EGztsMpbiIikk5ycjKSkpJM2jQajUW2HRYWhrCwsLrXMTExOHnyJFJTU7F69epmb4cJmoiI1MGCX4TWaDQWS8jNcf/992PXrl1mrcMETUREqqDme3Hn5OQgICDArHWYoImISBVE3eqzvLwcJ06cqHt9+vRp5OTkwMfHB507d0ZycjIuXLiAzz//HADwwQcfICQkBL169UJVVRU+/vhj7NixA99//71Z+2WCJiIiasT+/fvx0EMP1b2+de76+eefR1paGgoLC1FQUFD38xs3bmDq1Km4cOECWrdujcjISPzrX/8y2UZzMEETEZEqiJrgHjhwIIxGY4M/T0tLM3n92muv4bXXXrvj/TJBExGRKsj2NCt+D5qIiMgOsYImIiKVkKuEljJBb1qXhgOZ6Sg8fxatXDXo3rM3/jh+MgKCgkWHZlWxIW0RG+INn9atAACF1/T47sivyC+uEByZ9cjYZ0Defss6tv/Ti4O6YcbwHliVcRpzN+SLDseiZJviljJBHzmUjYeHPYWud4WjtrYGX362FAtmvYp3l62Fxs1ddHhWU1pZg415F3Gx/AYURcEDnbV4oV8nzNtxCoXXbogOzypk7DMgb79lHdu3RHbS4unozjh84aroUMgCpDwHPW3uIsQOGY6OwV3RuetdmJD0Bi6VFOHMiSOiQ7Oq3KJy5BVXoKSiGhfLb+Cb/BLoawzo4uO4v7hk7DMgb79lHdsA0NrVGR88ew+S1/0bZZXVosOxCkGPgxZGygT9e5UV5QAAjzZegiOxHQVAVEcvuDorOH25UnQ4NiFjnwF5+w3INbbnPBWBHYcvYvexS6JDsRpLPs1KDZo1xf3vf/8bERERcHKyTD7X6/UWf6xXSxkMBqxZkYrQ8EgEdekmOhyrC/TSYNqALnBxUqCvMWDl3vMocuApT0DOPgPy9vsWmcb28D4B6NXRCyNTzX+kIdmvZmXcPn364NdffwUAdO3aFZcu3dlfaPU95kuU1UtTcP7sKbw04x1hMdhS8TU9dDtOISXjDH48XYrnogLh7+kqOiyrkrHPgLz9vkWWsR3Q1g1vju6FKV/k4EaNQXQ4VqVY8D81aFYF3bZtW5w+fRodOnTAmTNnYDDc2Yegvsd8iUjSq5em4OefdiH5veXw8fWz+f5FqDUCJRXVAKpx7koVgr3d8VA3H/wjp0h0aFYjY58BefsNyDW2I4K08PXU4Jup/evaXJydcH9XH8T1D0bY9O9gaPgmWOqijrxqMc1K0P/1X/+FAQMGICAgAIqi4N5774Wzs3O97z116lST27P1Y75+z2g04otlC3AgKwMzdUvQ3j9QWCyiKQrg4iTXp17GPgNy9FvGsZ15/FcMfS/DpG3+2Ltx6mI5lm0/6TjJGdLl5+Yl6BUrVuDJJ5/EiRMn8Oqrr2LixInw9PS0dmxWs3pJCrIytiJhdgrc3D1w5fLNKfvWHh5w1bgJjs56nghvj/ziclyurIGbixPuDfJCqG9rLN59TnRoViNjnwF5+y3j2K7Q1+JYUblJW+WNWpRWVN/WTurS7O9BP/roowCAAwcOICEhQdUJesfmrwAA82a+ZNIenzgbsUOGiwjJJjw1LoiLCoSXmwuqagy4UKbH4t3ncKTEcW9eIWOfAXn7LevYloVarr62FLNvVPLpp59aIw6bSvt2r+gQhPh7dqHoEGxOxj4D8vZb1rH9e2MX7xEdglWo5eIuS+H3oImIiOyQlLf6JCIiFZKrgGaCJiIidZAsP3OKm4iIyB6xgiYiIlXgVdxERER2iFdxExERkXCsoImISBVkm+JmBU1ERGSHWEETEZEqsIImIiIi4VhBExGRKsh2FTcTNBERqQKnuImIiEg4VtBERKQKkhXQTNBERKQSkmVoTnETERHZIVbQRESkCryKm4iIyA7xKm4iIiISjhU0ERGpgmQFNBM0ERGphGQZmlPcRESkCooF/zPHzp07MWLECAQGBkJRFGzYsKHJddLT09G3b19oNBp0794daWlpZveXCZqIiKgRFRUVuPvuu7F48eJmvf/06dMYNmwYHnroIeTk5CAxMRETJkzA1q1bzdqvYjQajS0J2NIU2S7PIyJyILZIJVU1ltuWUquHXq83adNoNNBoNI2vpyj4+uuvMWrUqAbfM2PGDHz77bfIzc2ta/vv//5vXLlyBVu2bGl2jHZTQRuNRiFLVVUV3nzzTVRVVQmLgX1mv9ln9lvt/bYFNxfLLTqdDlqt1mTR6XQWiTMrKwuDBw82aRs6dCiysrLM2o7dVNCiXL16FVqtFmVlZfDy8hIdjk3I2GdAzn7L2GeA/Zat3y2h11uvgr7rrrswfvx4JCcn17Vt3rwZw4YNw/Xr1+Hu7t6sGHkVNxERSac5yVg0u5niJiIicgT+/v4oLi42aSsuLoaXl1ezq2eACZqIiMiioqOjsX37dpO2bdu2ITo62qztSJ+gNRoN3nzzTbuf6rAkGfsMyNlvGfsMsN+y9dvaysvLkZOTg5ycHAA3v0aVk5ODgoICAEBycjLi4uLq3v/iiy/i1KlTeO2113DkyBEsWbIE69atw5QpU8zar/QXiRERETUmPT0dDz300G3tzz//PNLS0jBu3DicOXMG6enpJutMmTIF+fn5CAoKwuzZszFu3Diz9ssETUREZIekn+ImIiKyR0zQREREdogJmoiIyA4xQUtk4MCBSExMFB0GCcTPgOMyGo3485//DB8fHyiKUnfFMakX7yRGROQAtmzZgrS0NKSnp6Nr167w9fUVHRLdISZoIiIHcPLkSQQEBCAmJkZ0KGQh0k5xb9myBf3790fbtm3Rrl07DB8+HCdPnhQdltXV1NRg8uTJ0Gq18PX1xezZs232JBqRDAYD5s+fj+7du0Oj0aBz587461//Kjosq6qoqEBcXBzatGmDgIAALFy4UHRIVmcwGKDT6RASEgJ3d3fcfffd+PLLL0WHZXXjxo3DK6+8goKCAiiKgi5duogOiSxA2gRdUVGBpKQk7N+/H9u3b4eTkxNGjx4Ng8EgOjSr+uyzz+Di4oKffvoJixYtwvvvv4+PP/5YdFhWl5ycjHnz5mH27NnIz8/HmjVr4OfnJzosq5o+fToyMjKwceNGfP/990hPT8fBgwdFh2VVOp0On3/+OZYtW4a8vDxMmTIFzz77LDIyMkSHZlWLFi3CnDlzEBQUhMLCQuzbt090SGQJRjIajUZjSUmJEYDx0KFDokOxmgEDBhh79uxpNBgMdW0zZsww9uzZU2BU1nf16lWjRqMxrly5UnQoNnPt2jWjq6urcd26dXVtly5dMrq7uxsTEhLEBWZFVVVVxtatWxszMzNN2uPj441jx44VFJXtpKamGoODg0WHQRYkbQV9/PhxjB07Fl27doWXl1fdlNCte6s6qn79+kFRlLrX0dHROH78OGprawVGZV2HDx+GXq/HoEGDRIdiMydPnsSNGzfwwAMP1LX5+PggLCxMYFTWdeLECVy/fh1DhgxBmzZt6pbPP/9citNX5HikvUhsxIgRCA4OxsqVKxEYGAiDwYCIiAjcuHFDdGhkYeY83o3Uq7y8HADw7bffomPHjiY/48MjSI2krKAvXbqEo0ePYtasWRg0aBB69uyJ0tJS0WHZxN69e01e79mzB6GhoXB2dhYUkfWFhobC3d39tse/ObJu3bqhVatWJse7tLQUx44dExiVdYWHh0Oj0aCgoADdu3c3WTp16iQ6PCKzSVlBe3t7o127dlixYgUCAgJQUFCAmTNnig7LJgoKCpCUlIQXXngBBw8exN/+9jeHv7rXzc0NM2bMwGuvvQZXV1c8+OCDKCkpQV5eHuLj40WHZxVt2rRBfHw8pk+fjnbt2qFDhw74y1/+Aicnx/2b3NPTE9OmTcOUKVNgMBjQv39/lJWVYffu3fDy8sLzzz8vOkQis0iZoJ2cnLB27Vq8+uqriIiIQFhYGD788EMMHDhQdGhWFxcXh8rKStx///1wdnZGQkIC/vznP4sOy+pmz54NFxcXvPHGG/jll18QEBCAF198UXRYVpWSkoLy8nKMGDECnp6emDp1KsrKykSHZVVz585F+/btodPpcOrUKbRt2xZ9+/bF66+/Ljo0IrPxcZNERER2yHHnu4iIiFSMCZqIiMgOMUETERHZISZoIiIiO8QETUREZIeYoImIiOwQEzQREZEdYoImIiKyQ0zQREREdogJmoiIyA4xQRMREdmh/w9n6o08xkfm+QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A @ A,square = True, \n",
    "            cmap = 'Blues',\n",
    "            annot = True, fmt = '.0f',\n",
    "            xticklabels = list(G.nodes), \n",
    "            yticklabels = list(G.nodes),\n",
    "            linecolor = 'k', linewidths = 0.2)\n",
    "plt.savefig('A @ A.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e32441d0-ffee-46c4-99f0-ff5d06286fac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 8., 13., 13., 11.,  8., 13.],\n",
       "        [13., 10., 14.,  7., 13., 11.],\n",
       "        [13., 14., 14., 11., 13., 14.],\n",
       "        [11.,  7., 11.,  4., 11.,  7.],\n",
       "        [ 8., 13., 13., 11.,  8., 13.],\n",
       "        [13., 11., 14.,  7., 13., 10.]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A @ A @ A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e13bcdd6-8c8a-4700-b390-00b9c34c9cc6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A @ A @ A,square = True, cmap = 'Blues', annot = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "93717e01-465c-48ba-bc54-af3b3da46b86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[12., 16., 17., 13., 12., 16.],\n",
       "        [16., 14., 18., 10., 16., 15.],\n",
       "        [17., 18., 19., 14., 17., 18.],\n",
       "        [13., 10., 14.,  7., 13., 10.],\n",
       "        [12., 16., 17., 13., 12., 16.],\n",
       "        [16., 15., 18., 10., 16., 14.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A + A @ A + A @ A @ A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "03b93c51-db92-4276-9878-3652851153ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A + A @ A + A @ A @ A,square = True, cmap = 'Blues', annot = True)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
